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Journal of Mathematical Sciences

, Volume 244, Issue 1, pp 22–35 | Cite as

Extremal quasiconformality vs bounded rational approximation

  • Samuel L. KrushkalEmail author
Article
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Abstract

We show that, on most of the hyperbolic simply connected domains, the weighty bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to the integral approximation). The obstructions are caused by the features of extremal quasiconformality.

Keywords

Rational approximation holomorphic function quasiconformal maps quasicircles universal Teichmüller space Schwarzian derivative Strebel point Grunsky coefficients 

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityBar-IlanIsrael
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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